Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C11×#423 ⋊ C2 |
| Sylow | C11 ⋊ #2925 |
392 conjugacy classes of subgroups.
| transitive degree | μt(G) = 704 |
Polycyclic presentation:
2^7,11|a^2=f,c^2=e,f^2=g,b^a=be,h^a=h^10,d^b=dg,h^b=h^10,d^c=dg,h^c=h^10190 conjugacy classes — view the full character table.
| maximal subgroup of | #14648077, #14648081, #14648091, … |
| maximal normal subgroup of | #14648077, #14648081, #14648091, … |
| maximal quotient of | #14751273, #14751327, #14751698, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 13178);